- Definitions
A random variable has a distribution if its probability density function is
where is a
The … See more
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The double exponential distribution, also known as the Laplace distribution, is a continuous probability distribution named after Pierre-Simon Laplace. It is characterized by its probability density function (PDF) and cumulative distribution function (CDF).
Probability Density Function (PDF)
The PDF of the Laplace distribution is given by: [ f(x \mid \mu, b) = \frac{1}{2b} \exp\left(-\frac{|x - \mu|}{b}\right) ] where:
( \mu ) is the location parameter (real number).
( b ) is the scale parameter (real number), sometimes referred to as the "diversity"2.
Cumulative Distribution Function (CDF)
The CDF of the Laplace distribution is: [ F(x) = \begin{cases} \frac{1}{2} \exp\left(\frac{x - \mu}{b}\right) & \text{if } x \leq \mu \ 1 - \frac{1}{2} \exp\left(-\frac{x - \mu}{b}\right) & \text{if } x \geq \mu \end{cases} ]
Properties and Applications
The Laplace distribution has several interesting properties and applications:
Double exponential distribution - Wikipedia
In statistics, the double exponential distribution may refer to Laplace distribution, or bilateral exponential distribution, consisting of two exponential distributions glued together on each side …
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1.3.6.6.12. Double Exponential Distribution
Jun 6, 2012 · Learn the definition, formula, and properties of the double exponential distribution, also known as the Laplace distribution. See plots, examples, and maximum likelihood estimators of the location and scale …
Laplace Distribution -- from Wolfram MathWorld
5 days ago · The Laplace distribution, also called the double exponential distribution, is the distribution of differences between two independent variates with identical exponential distributions. Learn its probability density function, …
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Apr 24, 2022 · The Laplace distribution, named for Pierre Simon Laplace arises naturally as the distribution of the difference of two independent, identically distributed exponential variables. …
15.7 Double Exponential (Laplace) Distribution - Stan
The double-exponential distribution can be defined as a compound exponential-normal distribution. Specifically, if \[ \alpha \sim \mathsf{Exponential}\left( \frac{1}{\lambda} \right) \] …
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Double Exponential (Laplace) distribution
Learn about the Double Exponential distribution, a continuous probability distribution with a location and a scale parameter. See its PDF, CDF, moments, usage, related distributions, and …
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The Laplace distribution is the distribution of the difference of two independent random variables with identical exponential distributions (Leemis, n.d.). It is often used to model phenomena with heavy tails or when data has a higher peak …
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The Laplace (or double exponential) distribution has the form of two exponential distributions joined back-to-back around a location parameter μ. It arises naturally as the difference …
Laplace (Double Exponential, Bilateral Exponential) Distribution
Laplace (Double Exponential, Bilateral Exponential) Distribution# \begin{eqnarray*} f\left(x\right) & = & \frac{1}{2}e^{-\left|x\right|}\\ F\left(x\right) & = & \left\{ \begin{array}{ccc} \frac{1}{2}e^{x} & & …
Statistics - Laplace Distribution - Online Tutorials Library
Laplace distribution represents the distribution of differences between two independent variables having identical exponential distributions. It is also called double exponential distribution. …
Chapter 2 Maximum Likelihood Estimation | Lecture 5 Note
The Laplace distribution is a continuous probability distribution. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions …
What is: Laplace Distribution - LEARN STATISTICS EASILY
The Laplace Distribution, also known as the double exponential distribution, is a continuous probability distribution characterized by its sharp peak at the mean and heavy tails. This …
The Double Exponential (Laplace) Distribution - search.r-project.org
The Double Exponential (Laplace) Distribution Description. Density, distribution function, quantile function and random generation for the double exponential distribution, allowing non-zero …
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The Laplace distribution, named for Pierre Simon Laplace arises naturally as the distribution of the difference of two independent, identically distributed exponential variables. For this reason, it is …
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Exponential growth and exponential decay are two of the most common applications of exponential functions. Systems that exhibit exponential growth follow a model of the form …
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Describes key properties of the Laplace distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
Notebook: The Laplace Distribution | Significance - Oxford Academic
Oct 4, 2018 · What is the Laplace distribution? The Laplace (or double exponential) distribution, like the normal, has a distinguished history in statistics. It has applications in image and …
What is the Laplace distribution? - TutorChase
The Laplace distribution, also known as the double exponential distribution, is a continuous probability distribution that is symmetric around its mean. It is often used in statistics to model …
Solved The Laplace distribution, also known as the double - Chegg
Find the mean and variance of the distribution. The Laplace distribution, also known as the double exponential distribution, has density function proportional to e^(-|x|) for all real x. There are 2 …
